Question

A circle has a radius of length r. If you mark off an arc on the circle of length 2r what is the measurement of the angle that subtends the arc?

A 2pi radians
B. 2 pi r radians
C. 2r radians
D. 2 radians

Answer 1

Answer: 2 radians

Explanation:

Answer 2

A full circle has a circumference of 2πr and an angle of 2π radians.

Set up a proportion:
2πr - 2π rad
2r - x rad


`2\pi r * x = 2\pi * 2 r \\ 2\pi r x=4 \pi r \\ x=(4 \pi r)/(2 \pi r) \\ x=2`

The answer is D. 2 radians.